Assessing pupil knowledge of the sequential structure of numbers

Research on children’s mental strategies for multidigit addition and subtraction identifies two categories of strategy. Collections-based strategies involve partitioning numbers into tens and ones, and can be modeled with base-ten materials. Sequence-based strategies involve keeping one number whole, and using the sequential structure of numbers. They can be modelled as jumps on an empty number line. Studies have found sequence-based strategies to be more successful, and to correlate with more robust arithmetic knowledge, particularly among low-attaining pupils. Studies also suggest that sequence-based strategies and sequential structure are not explicitly developed in many primary mathematics classrooms. This report draws on results from a three-year project which has the goal of developing pedagogical tools for intervention in the number learning of low-attaining third- and fourth- graders (8- to 10-year-olds). These tools include assessment tasks to inform intervention. The report focuses on four groups of assessment tasks that collectively enable detailed documenting of pupils’ knowledge of the sequential structure of numbers. Tasks and pupils’ responses are described in detail. Some examples follow. When asked to count back from 52, pupils said, ‘52, 51, 40, 49, 48, and so on’. When asked to count back by tens from 336, pupils had difficulty continuing after 326. Thus teen numbers in the hundreds (316) presented particular difficulties. Pupils had difficulty saying the number that is ten less than 306. Pupils had difficulty with locating the numbers 50, 25, 62 and 98 on a number line on which zero and 100 were marked. The report provides insight into assessing knowledge of sequential structure and argues that this is important basic number knowledge.